Q: Trouble using Samsung Syncmaster as External Monitor?

I hope someone can help.  I have a Late-2012 i7 Mac Mini.  My main display using the HDMI port, is an Acer 240HL 24". It has a Max Resolution of

1920x1080.  My goal is to run an External monitor to another room and Mirror the main display.  I have available, a Samsung Syncmaster 2033, 19-inch,

whose Max Resolution is 1600x900.

I tried running a long VGA cable with an adapter - to the Samsung monitor using the Mini's Thunderbolt (MiniDisplayPort).  When attempting the dual display

or mirroring, resolution on one or the other would not match - that is, either the main or external monitor appears distorted or shadowboxed. 

Is there no other alternative than to buy an absolutely identical monitor - that is - another Acer 240HL 24" in this case - to make this work? 

If there's any other solution, I'd welcome suggestions on how to make this work.

Thanks very much,

Mike